3(2p+7)-2(p+7)18p=

Solution for 3(2p+7)-2(p+7)18p= equation:

Simplifying
3(2p + 7) + -2(p + 7) * 18p = 0

Reorder the terms:
3(7 + 2p) + -2(p + 7) * 18p = 0
(7 * 3 + 2p * 3) + -2(p + 7) * 18p = 0
(21 + 6p) + -2(p + 7) * 18p = 0

Reorder the terms:
21 + 6p + -2(7 + p) * 18p = 0

Reorder the terms for easier multiplication:
21 + 6p + -2 * 18p(7 + p) = 0

Multiply -2 * 18
21 + 6p + -36p(7 + p) = 0
21 + 6p + (7 * -36p + p * -36p) = 0
21 + 6p + (-252p + -36p2) = 0

Combine like terms: 6p + -252p = -246p
21 + -246p + -36p2 = 0

Solving
21 + -246p + -36p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -82p + -12p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + -82p + -12p2)' equal to zero and attempt to solve:

Simplifying
7 + -82p + -12p2 = 0

Solving
7 + -82p + -12p2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.5833333333 + 6.833333333p + p2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + 6.833333333p + 0.5833333333 + p2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + 6.833333333p + p2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + 6.833333333p + p2 = 0 + 0.5833333333
6.833333333p + p2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
6.833333333p + p2 = 0.5833333333

The p term is 6.833333333p.  Take half its coefficient (3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
6.833333333p + 11.67361111 + p2 = 0.5833333333 + 11.67361111

Reorder the terms:
11.67361111 + 6.833333333p + p2 = 0.5833333333 + 11.67361111

Combine like terms: 0.5833333333 + 11.67361111 = 12.2569444433
11.67361111 + 6.833333333p + p2 = 12.2569444433

Factor a perfect square on the left side:
(p + 3.416666667)(p + 3.416666667) = 12.2569444433

Calculate the square root of the right side: 3.500991923

Break this problem into two subproblems by setting 
(p + 3.416666667) equal to 3.500991923 and -3.500991923.

Subproblem 1
p + 3.416666667 = 3.500991923

Simplifying
p + 3.416666667 = 3.500991923

Reorder the terms:
3.416666667 + p = 3.500991923

Solving
3.416666667 + p = 3.500991923

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-3.416666667' to each side of the equation.
3.416666667 + -3.416666667 + p = 3.500991923 + -3.416666667

Combine like terms: 3.416666667 + -3.416666667 = 0.000000000
0.000000000 + p = 3.500991923 + -3.416666667
p = 3.500991923 + -3.416666667

Combine like terms: 3.500991923 + -3.416666667 = 0.084325256
p = 0.084325256

Simplifying
p = 0.084325256

Subproblem 2
p + 3.416666667 = -3.500991923

Simplifying
p + 3.416666667 = -3.500991923

Reorder the terms:
3.416666667 + p = -3.500991923

Solving
3.416666667 + p = -3.500991923

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-3.416666667' to each side of the equation.
3.416666667 + -3.416666667 + p = -3.500991923 + -3.416666667

Combine like terms: 3.416666667 + -3.416666667 = 0.000000000
0.000000000 + p = -3.500991923 + -3.416666667
p = -3.500991923 + -3.416666667

Combine like terms: -3.500991923 + -3.416666667 = -6.91765859
p = -6.91765859

Simplifying
p = -6.91765859

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.084325256, -6.91765859}
Solution
p = {0.084325256, -6.91765859}